24 Optimizing Optimization
of optimization in the financial world has been less than remarkable. While
the practice of using optimization-based techniques in constructing portfolios
has gained wide acceptance in the past decade, it has still not reached its full
potential. The community of portfolio managers (PMs) continues to perceive
optimizers as black box tools that only partly capture the complexities of real-
world portfolios. We believe that there are two factors that have hindered the
growth of financial optimization.
First , unlike other application areas, uncertainty has a focal position in the
world of financial optimization. Risk management, the practice of managing
and controlling the inherent stochastic nature of portfolio returns, is an indis-
pensable component of any quantitative model. It entails complex interaction
between statistics and optimization, and is often encumbered with problems
ranging from parameter misestimation to overfitted models. With the emer-
gence of global markets, fading international trading boundaries, and current
economic turbulence, the risk model business itself has undergone a paradigm
shift. A contemporary PM trading in stocks on NYSE to Nikkei needs access
to a robust risk model that can provide multiple views of risk, and can quickly
adapt to the ever-changing financial landscape. These factors make software
design for financial optimization extremely challenging.
Second , constructing an optimal portfolio is only one aspect of the practice
of portfolio management. An optimized portfolio often undergoes a series of
refinements and alterations each of which addresses a practical concern that
was not captured by the underlying mathematical model. As appealing as it
may seem, a single optimal portfolio hardly provides any insight to comple-
ment the tremendous amount of expertise it takes to mutate the output of a
black box solver into a practically tradable portfolio. For instance, it offers
little insight into the manner in which the constraints present in the strategy
affect the choice of the optimal portfolio. While some of the constraints in a
strategy, such as budget constraint, are mandatory, several others just repre-
sent tentative guidelines that the PM is expected to follow. A single optimal
portfolio restricts the PM from exploring portfolios that violate some of these
tentative constraints but have other extremely desirable characteristics such
as expected return, transfer coefficient, implied beta, etc. To overcome these
shortcomings, software providers need to break from the image of being black
box optimizers and design flexible products that assist the PM in portfolio
design from inception through trade execution.
As a leading provider of portfolio optimization tools, Axioma has under-
taken several initiatives to address these concerns. Our product suite employs
ideas from robust optimization to tackle parameter misestimation problems,
thereby giving rise to portfolios that are less sensitive to estimation errors. Our
“ Robust ” risk models are updated on a daily basis to reflect the latest changes
in the financial markets across the globe. Our modeling environment allows
PMs to incorporate multiple risk models, thereby giving them a better risk
assessment. This chapter offers a snapshot of the latest research developments
at Axioma that further enhance our capacity to address challenging problems
in financial optimization. The rest of the chapter is organized as follows.